The mayoral candidates support that figure, but now some politicians think other basic city services could benefit if the force was slightly smaller.

In 1989, then-Los Angeles Councilman Zev Yaroslavsky unveiled an audacious plan to boost the city police force by more than 25% to 10,000 officers.

He couldn't have imagined that city leaders would chase that goal for nearly a quarter of a century until, at the start of this year, Mayor Antonio Villaraigosa announced that he had pushed the LAPD over the long-elusive benchmark.

The two candidates vying to replace Villaraigosa in the May 21 election — City Controller Wendy Greuel and Councilman Eric Garcetti — have embraced the mayor's achievement, crediting the LAPD buildup in large measure for the city's lowest crime rates since the 1950s. Indeed, Greuel has committed to enlarging the police force an additional 20%, if the city treasury grows.

But increasingly, voices on the periphery of the mayoral campaign argue that rising police costs — up 36% to more than $2 billion over the last eight years, more than twice the rate of growth in such discretionary spending overall — raises two critical questions: Has the expansion been crucial to making Los Angeles safer? Has the relentless pursuit of more officers come at too great a cost to paramedic response times, paving streets and other basic services?

Among those raising such concerns are former police chief and current Councilman Bernard C. Parks, Councilman Paul Koretz, former first deputy mayor and businessman Austin Beutner, the police officers' union and, in a small irony, Yaroslavsky.

"If the Police Department does not lose any officers over the next few years, during this time of economic hardship, it's because the rest of city services have been eviscerated," said Yaroslavsky, now a Westside and San Fernando Valley representative on the county Board of Supervisors. "I don't think it's sensible to say that we cannot cut the Police Department by even one position."

There is little consensus among criminal-justice academics about the effect that changes in police staffing have on crime rates. Where officers are deployed and the assignments they are given appear to be as important as the number of cops on the payroll, said Jeremy M. Wilson, a Michigan State University criminologist. A recent report on police staffing levels coauthored by Wilson suggested that many departments simply guess the number of officers needed. "We determine how many officers we need," said one police official in the report, "by holding an envelope to our head."

Many criminologists who have studied big-city crime decreases credit longer prison sentences and the retreat of the crack-cocaine epidemic, among other reasons, as being most responsible for bringing down crime. They point to cities such as Seattle and Dallas that cut police staffing in the 1990s and still saw crime drop sharply.

But LAPD Chief Charlie Beck argues that there is an important correlation between officer staffing levels and lower crime rates. Cities such as San Jose, Long Beach and Oakland saw crime surge after cutting their police forces, he said.

Villaraigosa, whose legacy is tied to his record of expanding the Police Department, despite the Great Recession, also draws a direct line between more cops and less crime. The city has had fewer than 300 murders each of the last three years, he notes, down from a high of nearly 1,100 in 1992.

"The numbers speak for themselves," Villaraigosa said. "A 49% drop in violent crime and homicides, a 66% drop in gang homicides. Growing our Police Department and ... community policing is a big reason why we are safer today."

But why 10,000 cops for L.A.?

Yaroslavsky latched onto the number after crack- and gang-fueled violent crime surged. Voters demanded action. The 10,000 figure lacked any analytical underpinning but was "a nice round number," Yaroslavsky chuckled in an interview. It also "takes the force from four digits to five digits." The goal stuck, becoming a lodestar of L.A.'s mayoral politics ever since.

Police Chief Willie L. Williams, hired three years after Yaroslavsky rolled out his plan, said he wanted to reach the mark by 2000. In 1993, mayoral candidate Richard Riordan suggested pushing the force past 10,000 officers by leasing Los Angeles International Airport to a private operator and diverting the income to the LAPD. His opponent, Councilman Michael Woo, pledged to reach the 10,000-officer target by shifting money away from other departments. Riordan won the contest but never added the 3,000 officers he had promised.